Optimal. Leaf size=16 \[ -\frac {\left (a+\frac {b}{x}\right )^9}{9 b} \]
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Rubi [A] time = 0.00, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {261} \[ -\frac {\left (a+\frac {b}{x}\right )^9}{9 b} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin {align*} \int \frac {\left (a+\frac {b}{x}\right )^8}{x^2} \, dx &=-\frac {\left (a+\frac {b}{x}\right )^9}{9 b}\\ \end {align*}
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Mathematica [B] time = 0.01, size = 96, normalized size = 6.00 \[ -\frac {a^8}{x}-\frac {4 a^7 b}{x^2}-\frac {28 a^6 b^2}{3 x^3}-\frac {14 a^5 b^3}{x^4}-\frac {14 a^4 b^4}{x^5}-\frac {28 a^3 b^5}{3 x^6}-\frac {4 a^2 b^6}{x^7}-\frac {a b^7}{x^8}-\frac {b^8}{9 x^9} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.99, size = 88, normalized size = 5.50 \[ -\frac {9 \, a^{8} x^{8} + 36 \, a^{7} b x^{7} + 84 \, a^{6} b^{2} x^{6} + 126 \, a^{5} b^{3} x^{5} + 126 \, a^{4} b^{4} x^{4} + 84 \, a^{3} b^{5} x^{3} + 36 \, a^{2} b^{6} x^{2} + 9 \, a b^{7} x + b^{8}}{9 \, x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 14, normalized size = 0.88 \[ -\frac {{\left (a + \frac {b}{x}\right )}^{9}}{9 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.01, size = 91, normalized size = 5.69 \[ -\frac {a^{8}}{x}-\frac {4 a^{7} b}{x^{2}}-\frac {28 a^{6} b^{2}}{3 x^{3}}-\frac {14 a^{5} b^{3}}{x^{4}}-\frac {14 a^{4} b^{4}}{x^{5}}-\frac {28 a^{3} b^{5}}{3 x^{6}}-\frac {4 a^{2} b^{6}}{x^{7}}-\frac {a \,b^{7}}{x^{8}}-\frac {b^{8}}{9 x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.10, size = 14, normalized size = 0.88 \[ -\frac {{\left (a + \frac {b}{x}\right )}^{9}}{9 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.10, size = 88, normalized size = 5.50 \[ -\frac {a^8\,x^8+4\,a^7\,b\,x^7+\frac {28\,a^6\,b^2\,x^6}{3}+14\,a^5\,b^3\,x^5+14\,a^4\,b^4\,x^4+\frac {28\,a^3\,b^5\,x^3}{3}+4\,a^2\,b^6\,x^2+a\,b^7\,x+\frac {b^8}{9}}{x^9} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.69, size = 95, normalized size = 5.94 \[ \frac {- 9 a^{8} x^{8} - 36 a^{7} b x^{7} - 84 a^{6} b^{2} x^{6} - 126 a^{5} b^{3} x^{5} - 126 a^{4} b^{4} x^{4} - 84 a^{3} b^{5} x^{3} - 36 a^{2} b^{6} x^{2} - 9 a b^{7} x - b^{8}}{9 x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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